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Q: Linear Equation x? dy – sin3x dx + 2xy dx = (final answer should be in terms of 0)

A: We have to solve

Q: .x = t² – 2t – 11 and y = t(t – 4)³ – 3t²(t – 4)² + 7

A: Given:- x = t² - 2t - 11 and y=t(t-4)³ - 3t²(t-4)² +7 To find:- y' 

Q: Prove that 1-x 1+x -1 cos'x = 2 sin V 2 2cos 2

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Q: Compute the area bounded by the functions: 3y and x = y? - 10

A: From the given functions the bounded region is as shown below. Now find the point of intersection o...

Q: 1. (a) Find the differential of g(u, v) = u² + uv. (b) Use your answer to part (a) to estimate the c...

A: Here we have to find the differentials of g(u,v)=u2+uv .

Q: 1. The area of an ellipse is A = nab. Find the dimensions a and b that produce the maximum area if t...

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Q: Find the value, correct to 3 decimal places for each expression: (a) sec(arctan(2)) (b) cos(2 sin())...

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Q: Let R be the region bounded by y = 6.5 – x, the x axis and the y axis. 6 4 3 2 1 The solid obtained ...

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Q: (b) Find the area of the region between the x-axis and the graph of f(x)=3x² - 3, where -2<x<2

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Q: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) y = 19k

A: The objective of the question is find the orthogonal trajectories of the family of the curves.

Q: 4. sin Tx - y =0 4 5. --y = -1

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Q: Find b and c so that y = 7x2 + bx + c has vertex (– 6, 2). - С —

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Q: dy and check your result using dx Use the following theorem to find implicit differentiation. If the...

A: To find the dy/dx using the given theorem   

Q: Determine the equation of the curve at every point of which the tangent line has a slope of 2x.

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Q: Find a unit vector in the direction in which f(x,y, z) + %3D increases most rapidly at P(1, 2, -2), ...

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Q: 3. Find the matrix E-l where 1 0 01 E = 1 -4 0 1 ......

A: Given that: E=100010-401

Q: Solve the given differential equation. (x² + 2y)dx – xdy = 0 4 O 2y = x* + cx² - 2 O 2y = x* + cx

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Q: Consider a rectangular metal box without a top lid which, because of being heated, is increasing in ...

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Q: 4. Use transformations of the graph of e* to graph the functionf(x) = e¯* – 3 and state the domain, ...

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Q: Show that f, given by f ( x) = x- |x| (x+ 0) is continuous on R-{0}

A: Continuity

Q: 2x Evaluate / 2r+3 dx 3log(2x+3) + C X - -2 O x – 3log(2x + 3) + C O None 3log(2x+3) х — + C 2

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Q: An object's velocity function is given by v (t) = sin(2t – 1). At time t = 0, the object's position ...

A: Explanation of the answer is as follows

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the s...

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Q: Prove that 1-x 1+x -1 cos'x = 2 sin V 2 2cos V 2 COS OS

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Q: = 2. Find h'(4). Suppose that f(4) = 3, g(4) = 4, f'(4) = -5, and g'(4) (a) h(x) = 2f(x) + 5g(x) %3D...

A: As per Bartley guidelines we are supposed to answer only 3 subparts of a question per post. This pos...

Q: Find L{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) =...

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Q: Find local maximum or local minimum of p p 2'2 f(x) = - sin 2x - x defined on

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Q: 4 у3 2) S-sy dy 2-5y4

A: Please see the below picture for detailed solution. 

Q: Given that f(7) = 1 and f'(7) = -7, find an equation for the tangent line to the graph of y = f(x) a...

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Q: I, \B|, A + B, and |A + B|. Then verify -1 1 8. 1 0 1 A = 0 1 1 B = -1 1 8 1 1 -1 0 1 8

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Q: The radius of the largest sphere with center (29,330,290) that is contained in the first octant is e...

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Q: V3x2+x 4) lim X00

A: To evaluate the given limit first  we simplify the given rational function and then substitute x = ∞

Q: Consider the function. f(x, y) = 17 - X 3 2 - Find Duf(2, 5), where u = cos(e)i + sin(0)j. (a) 4 Duf...

A: Explanation of the answer is as follows

Q: Find the solution of the differential equation that satisfies the given initial condition. dy xe", y...

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Q: 4. хdy— ydx %3 (х — 1)е* dx

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Q: 13. Test the series for convergence or divergence. (-6)**1 *-1 48

A: Given series is ∑m=1∞-6m+148m To establishe the convergence of given series we are using the result ...

Q: Find two positive integers x and y such that x + y = 60 and xy² is maximum

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Q: f(x+h)-f(x) If '(x) using the definition f '(x) = lim %3D h h→0 e graph of y = v5x + 11 at x = 1. En...

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Q: 11. Given, f(x) = 5x + 3. What is the value of f"(x)? A. -5 В. -3 С. 3 D. 5

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Q: Sin 10. Im sin ax 12.lim X-0 sinbr X-0

A: We have to find

Q: Find the distance from the point (- 4, 21, – 5) to the given plane or axis. If required, round your ...

A: As per the guidelines I am supposed to do first three questions of a multipart questions. So I am so...

Q: Q1. Let f: R² → R be defined by 2x2y if (x, y) # (0,0), f (x, y) = { x4 + y² if (x, y) = (0,0). (a) ...

A: According to our guidelines we can answer only three subparts, or first question and rest can be rep...

Q: w đô hegative signs act graphs? c. What differences do you notice between the graphs of x2 and – x2 ...

A: Given: c) x2 and -x2      If the negative sign belongs to the y, then the graph will flip about the ...

Q: 2. Solve ydx – (eu + 2xy – 2x) dy = 0.

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Q: x+1 if'(1) 2. f(x) = x² – 4x + 1 ; f'(2) 2x 1. f(x) = ; f'(1) 3. f(x) = Vx + 8 ;f'(1)

A: According to our guidelines, we can answer only the first problem or three subparts of a problem, th...

Q: Show that f, given by f ( x) x-|x| x* 0) is continuous on R-{0}

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Q: What is the average value of f (x) = 3x² on [–4, 0]?

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Q: (x + sin y)dx + (x cos y – 2y)dy = 1 x² – 2 æ sin y + y = c 1 a² + x sin y – y² = c 1 x² – x sin y –...

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Q: Find the standard equation of the parabola. The height is 50 feet and the base width is 30 feet. Use...

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Q: y '4Gy= e+ Y (6)= 2

A: A detailed solution is given below   (As per our guidelines we are supposed to answer only one quest...